TY - JOUR
T1 - The High Order Block RIP Condition for Signal Recovery
AU - Li , Yaling
AU - Chen , Wengu
JO - Journal of Computational Mathematics
VL - 1
SP - 61
EP - 75
PY - 2018
DA - 2018/08
SN - 37
DO - http://doi.org/10.4208/jcm.1710-m2017-0175
UR - https://global-sci.org/intro/article_detail/jcm/12649.html
KW - Block sparsity, Block restricted isometry property, Compressed sensing, Mixed
$l_2/l_1$ minimization.
AB - <p style="text-align: justify;">In this paper, we consider the recovery of block sparse signals, whose nonzero entries
appear in blocks (or clusters) rather than spread arbitrarily throughout the signal, from
incomplete linear measurements. A high order sufficient condition based on block RIP
is obtained to guarantee the stable recovery of all block sparse signals in the presence
of noise, and robust recovery when signals are not exactly block sparse via mixed $l_2/l_1$ minimization. Moreover, a concrete example is established to ensure the condition is
sharp. The significance of the results presented in this paper lies in the fact that recovery
may be possible under more general conditions by exploiting the block structure of the
sparsity pattern instead of the conventional sparsity pattern.</p>